Izvestiya of Saratov University.

Physics

ISSN 1817-3020 (Print)
ISSN 2542-193X (Online)

For citation:

Shabunin A. V. Determining the structure of couplings in chaotic and stochastic systems using a neural network. Izvestiya of Saratov University. Physics , 2025, vol. 25, iss. 3, pp. 277-287. DOI: 10.18500/1817-3020-2025-25-3-277-287, EDN: EXCZHP

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
29.08.2025
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Language: 
Russian
Heading: 
Theoretical and mathematical physics
Article type: 
Article
UDC: 
517.9:621.372
DOI: 
10.18500/1817-3020-2025-25-3-277-287
EDN: 
EXCZHP

Determining the structure of couplings in chaotic and stochastic systems using a neural network

Autors: 
Shabunin Alexey Vladimirovich, Saratov State University
Abstract: 

Subject and Objectives: The purpose of this work is development and research of an algorithm for determining the structure of couplings of an ensemble of chaotic self-oscillating systems with and without noise, which is based on artificial neural networks (ANN). Ensembles of two cubic maps with diffusive unidirectional and mutual couplings are the systems under study. Materials and Methods: The method is based on the determination of causality by Granger and the use of direct propagation artificial neural networks trained with regularization. Results: The applicability of the algorithm has been considered both for a strictly deterministic system and for a system with low-intensity additive Gaussian noise. The results have shown the possibility of using ANN to identify the degree of influence of the subsystems on each other, as well as to assess the magnitude of the coupling coefficients. At the same time, low-intensity noise demonstrates a minor effect on the measurement results. Moreover, noise can play a constructive role, allowing to determine the connectivity in the cases where measurements become impossible in “pure” systems, for example, in the chaos synchronization mode or in the case of regular modes. Discussion and Conclusions: Although the method has shown its effectiveness for simple mathematical models, its applicability for real systems depends on a number of factors, such as sensitivity to external noise, distortion of the waveforms, the dimension of the array etc. These questions require additional research.

Key words: 
nonlinear dynamics
ensembles of chaotic systems
determination of connectivity
artificial neural networks
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Received: 
26.03.2025
Accepted: 
15.05.2025
Published: 
29.08.2025
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